Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three

For any bounded smooth domain Omega subset of R-3 (or Omega = R-3), we establish the global existence of a weak solution (u, d) : Omega x [0, +infinity) -> R-3 x S-2 of the initial boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data (u(0), d(0)) is an element of H x H-1 (Omega, S-2), with d(0) (Omega) subset of S-+(2) (the upper hemisphere). Furthermore, (u, d) satisfies the global energy inequality (1.4). (C) 2016 Wiley Periodicals, Inc.